This invention relates to an improved apparatus for reconstructing a two-dimensional image of an object slice from linear projection data. More specifically, the invention relates to reconstruction of images which are free from artifacts due to filtration truncation errors.
The preferred embodiments of the invention will be described with reference to X-ray projection data obtained using transmission computerized tomography (CT). The invention, however, is not so limited and may be practiced with data obtained by other suitable methods such as ultrasonic scanning, computed emission tomography, and nuclear magnetic resonance. Moreover, the invention is not limited to data obtained by medical diagnostic apparatus, but is applicable to data obtained by any method where errors result from truncation of data.
In medical diagnostic applications, the projection data obtained by any of the aforementioned modalities are processed with the aid of digital-processor means in accordance with basic techniques well known to the art to produce the desired images. A preferred image reconstruction technique utilized in CT employs convolution and backprojection of the data. A detailed description of this and other suitable reconstruction techniques is provided by R. A. Brooks and G. Di Chiro in "Principles of Computer-Assisted Tomography (CAT) and Radiographic and Radioisotopic Imaging," Phys. Med. Biol., Vol. 21, No. 5, pp. 689-732, 1976.
Briefly, in one preferred embodiment of a scan geometry utilized in CT, the X-ray source is mounted on a scanner base that is journalled for rotation about the nominally horizontal axis on a tiltable gantry. A multiple-cell X-ray detector is mounted on a scanner base on the opposite side of the axis from the X-ray source. The X-ray beam emanating from the source is collimated into a fan-shaped configuration that spreads over the circumferential length of the detector and is fanned in the direction to which the rotational axis of the scanner base is perpendicular. The patient to be examined is customarily supported on an X-ray-transmissive table top or cradle in coincidence with the rotational axis of the scanner. In the course of an examination, the X-ray source and detector orbit jointly about the patient so that the detector will be able to produce signals (referred to as raw data) representative of X-ray beam attenuated by the patient for a multiplicity of paths between the X-ray source and detector. The detector signals are sampled during a scan, such that at a given time all of the sampled detector outputs are referred to as either a projection or a view. The signals representative of beam attenuation are acquired by a data acquisition system and variously processed and backprojected to yield digital data representative of the intensity of the picture elements that comprise the image of the body layer that has been scanned. The picture element data is converted to analog video signals and is used to display the image on a video monitor.
The processing of the raw data prior to backprojection can be divided into a preprocessing step and a filtration step. The raw attenuation data is preprocessed to provide line-integral projection data. The preprocessed data is then also typically filtered by one of various methods described in the above-referenced article. A preferred filtering operation requires convolving the preprocessed projection data with a kernel function prior to the operation of backprojection to create an image. The application of convolution to the image reconstruction process is disclosed in detail in U.S. Pat. No. 4,149,248, issued Apr. 10, 1979 to Pavkovich and which is assigned to the same assignee as the present invention. This patent is incorporated herein by reference as background information.
Typically, the convolution operation is implemented by taking the discrete Fourier transform (DFT) of the preprocessed projection data, multiplying it by the DFT of the kernel function, and, finally, obtaining the filtered projection data by taking the inverse DFT (IDFT) of the product. It should be noted that DFT's are performed using a fast Fourier transform algorithm commonly denoted FFT.
The projection preprocessing and the filtration operations are implemented using what will be referred to as a high-precision array processor. Such an array processor uses, for example, a 38-bit floating point number representation with 28 of the 38 bits used to represent the mantissa. In some CT system configurations, it is desirable to perform the preprocessing operations in one array processor and to perform the filtration operations in a second array processor. The second array processor can be optimized for DFT's using, for example, a 22-bit floating point representation with a 16-bit mantissa. Because of the reduced accuracy of the second processor, when compared to the high-precision processor, the resulting filtered projection data contains what will be referred to as filtration truncation errors. The truncation errors arise due to the decreased number of bits used to represent the mantissa in the lower precision processor. The effects of truncation errors have been reviewed, without suggesting a solution in accordance with the invention, in A. V. Oppenheim and R. W. Schafer, "Digital Signal Processing," Prentice-Hall, 1975.
Structured or correlated noise appears in the filtered projection data because similar truncation errors are made when filtering each preprocessed projection. The backprojection process enhances the projection-to-projection correlated noise, thus causing structured noise such as rings and center spots in the image.
It is, therefore, a principal object of the invention to provide a method to reduce the errors caused by truncation in a limited precision array processor when using it to convolve data using Fourier techniques.